Hierarchically Coordinated Energy Management for A Regional Multi-microgrid Community
11 Hierarchically Coordinated Energy Management forA Regional Multi-microgrid Community
Chengquan Ju
Abstract —This paper proposes a novel hierarchically coordi-nated energy management system (EMS) for a regional com-munity (e.g., residential area, campus, industrial park, etc.)comprising multiple small-scale microgrids (MGs) (e.g., houses,buildings, etc.). It aims to minimize the total operational costof the MG community and maximize the individual benefit ofeach MG simultaneously. At the local level inside each MG,with the detailed modeling of various energy resources includingphotovoltaics (PVs), energy storages (ESs), electric vehicles (EVs)and dispatchable loads, the individual optimization problem isformulated as a mixed-integer linear program (MILP). LocalEMSs makes power dispatch decisions for all the controllableunits to minimize the operational cost in individual MGs. Atthe community level, a novel pairing algorithm is proposedto explicitly find the MG pairings with surplus and deficit.The community-level EMS employs the pairing algorithm todetermine specific power exchanges among MGs and minimizesthe energy transactions with the upstream grid. The operationalcost of each individual MG is further reduced by additionaleconomic benefits procured by the community-level EMS. Theproposed method has distinguishing advantages on modelinggenerality, computational complexity and privacy protection, andits performance is verified by the simulation results.
Index Terms —Energy management, microgrids, hierarchicaloptimization, energy transaction. N OMENCLATURE
A. Indices and Sets Δ 𝑡 Time interval. 𝑡 Index of time. 𝑖, 𝑗
Indices of MG. 𝑘 Index of controllable appliances. 𝑛 Index of special ordered set of type 2 (SOS-2). 𝑵 𝑮 Set of MGs. 𝑬𝑺 𝒊 Set of Energy Storages (ESs) in MG 𝑖 . 𝑬𝑽 𝒊 Set of Electric Vehicles (EVs) in MG 𝑖 . 𝑳 𝒊 Set of type 1 loads in MG 𝑖 . 𝑳 𝒊 Set of type 2 loads in MG 𝑖 . 𝑵 𝒊𝒌 SOS-2 for 𝑘 th ES in MG 𝑖 . B. Decision Variables 𝑝 𝑖,𝑡𝑀,𝑏 , 𝑝 𝑖,𝑡𝑀,𝑠 Purchasing and selling power of upstream grid. 𝑝 𝑖 𝑗,𝑡𝐶,𝑏 , 𝑝 𝑖 𝑗,𝑡𝐶,𝑠 Transmitted power between MG 𝑖 and 𝑗 . 𝑝 𝑖,𝑡𝑘,𝑏 , 𝑝 𝑖,𝑡𝑘,𝑠 Discharging and charging power of ES (EV). 𝑢 𝑖,𝑡𝑀 Binary indicator for power from utility grid. 𝑢 𝑖 𝑗,𝑡𝐶 Binary indicator for transmitted power between 𝑖 th and 𝑗 th MG. 𝛿 𝑖,𝑡𝑘 Binary indicator for power of ES. 𝜃 𝑖,𝑡𝑘 Binary indicator for power of EV. 𝜆 𝑖,𝑡𝑘 Binary indicator for type 1 load. 𝜇 𝑖,𝑡𝑘 Binary indicator for type 2 load. 𝜈 𝑖,𝑡𝑘,𝑠 , 𝜈 𝑖,𝑡𝑘,𝑒 Integral variables to indicate starting and endingtime of 𝑘 th type 2 load. 𝛼 𝑖,𝑡𝑘,𝑛 Element in SOS-2 𝑵 𝒊𝒌 of 𝑘 th ES. C. Parameters 𝑁 𝑔 Number of MGs. 𝑇 Length of time horizon. 𝑐 𝑡𝑏 , 𝑐 𝑡𝑠 Electricity purchasing and selling price betweenindividual MGs and the upstream grid. 𝑐 𝑡𝐶 Electricity transaction price between MGs in thecommunity. 𝜀 𝑖 𝑗 Loss factor between MG 𝑖 and 𝑗 . 𝑃 𝑖𝑀 , 𝑃 𝑖𝑀 Power limits of utility grid. 𝑝 𝑖,𝑡𝐶 Aggregation of transmitted power in community. 𝑃 𝑖 𝑗𝐶 , 𝑃 𝑖 𝑗𝐶 Transmitted power limits. 𝑃 𝑖,𝑡𝑘 , 𝑃 𝑖,𝑡𝑘 ES (EV) power limits. 𝜁 𝑖𝑘 ES (EV) charging/discharging efficiency. 𝐸 𝑖,𝑡𝑘 ES (EV) energy level. 𝐸 𝑖𝑘 , 𝐸 𝑖𝑘 ES (EV) energy limits. 𝐸 𝑖,𝑑𝑒𝑝𝑘 EV energy requirement at departure. 𝑻 𝒊𝒌 Set of Parking time region. 𝑝 𝑖,𝑡𝐿 Power of non-dispatchable loads. 𝑝 𝑖,𝑡𝑃𝑉 Power of PV. 𝑝 𝑖,𝑡𝑘 Power of type 1 and 2 loads. 𝑃 𝑖𝑘 Total required energy of type 1 and 2 loads. 𝐻 𝑖𝑘 Operation durations of 𝑘 th type 1 (or 2) load sets. 𝑐 𝑖𝑘,𝑛 ES degradation cost coefficient. 𝐺 𝑖𝑘,𝑛 Energy level in which 𝑐 𝑖𝑘,𝑛 ∈ 𝑵 𝒊𝒌 . 𝑙 𝑥𝑖 , 𝑙 𝑦𝑖 Coordinates of 𝑖 th MG. 𝑊 Weighting matrix of MG community. 𝑤 𝑖 𝑗 Weighting coefficient between MG 𝑖 and 𝑗 . D. Functions 𝑓 𝑘 (•) ES degradation cost. 𝐹 (•) Linearized ES degradation cost.I. I
NTRODUCTION
Microgrid (MG) is generally described as an independentsmall-scale power system at the downstream of the distributionsystem. Existing in different forms such as individual houses,commercial/residential buildings and so on [1]–[3], MGs in-clude a variety of distributed energy resources (DERs), e.g.photovoltaics (PVs), wind turbines (WT) and microturbines(MT), energy storages (ESs) and electric vehicles (EVs), andcan operate both in the islanded mode and in conjunction withthe upstream electricity grid depending on different operating a r X i v : . [ ee ss . S Y ] F e b requirements [4], [5].Regional MG community, such as residential area, uni-versity campus, industrial park and so on, clusters a groupof MGs under the single point of common coupling (PCC)to consolidate system reliability and economy. In normaloperational conditions, MG community helps individual MGsreduce transmission losses and enhance system reliability bysharing resources internally [6]. Under extreme circumstances,MG community can operate as an autonomous entity out ofthe upstream power grid to maintain its integrity and security.Several recent studies have shown significances of MG com-munity on power quality and system reliability improvements[7]–[9].Energy management is the core component to improveenergy efficiency, increase economic benefit and maintainoperation reliability. Generally, energy management system(EMS) is classified into centralized and decentralized forma-tions by different topology frameworks and control strategiesto emphasize specific problems such as energy efficiency,system robustness and so on [10]–[12], in which the central-ized scheme often requires full information from dispatchablecomponents and to make decisions for each individual entity.However, with the size expansion of the MG communityand increasing variety of power electronic components, thescheduling policy on operational strategies may become expo-nentially complex since intensive computation capability areoften required. Inconsistent optimization objectives of differentMGs and information security/privacy issues may also beserious concerns that hinder centralized energy managementdeployment into the MG community.Several recent studies have focused on various decentralizedmanagement schemes for MG community that require mul-tiple entities to cooperate and coordinate in different levels,from various aspects such as cost minimization [13]–[15],coalitional transaction [16], [17] and so forth. For example,a control strategy for coordinated operation is proposed in[18] to minimize the operational cost in a distribution systemby decomposing decision-making process into multiple stages.A coordinated strategy for optimal energy management inmulti-MG systems is presented in [19] by introducing theprobabilistic index for cost minimization. Different algorithmsfor multi-MG coordination have been also investigated [20],[21].Existing studies have provided profound concepts to co-ordinated operation for MG community, however, they havelimited consideration in several aspects as follows:1) Optimization objectives of individual MGs may be incon-sistent with each other as they are considered as self-interestedentities. Various infrastructures of MGs would challenge theimplementation of EMS in the sense of complexity on opera-tional strategies.2) Existing optimization frameworks may fall into thecurse of dimensionality, since they usually require intensivecomputation capability, especially for a large size of MGscommunity. Convexity issues for large-size problems may alsomake optimal solutions intangible [22].3) Requirements for full observability in the centralizedEMS and extensive information exchange in the decentralized EMS would introduce MG security and privacy issues.To overcome the above drawbacks, we propose a hierar-chically coordinated EMS model to establish an effective andcomputationally efficient mechanism of power scheduling forindividual MGs as well as energy transactions inside MGcommunity. In contrast to previous existing studies, the maincontributions are summarized as follows.1) A hierarchically coordinated EMS for a regional com-munity comprising multiple small-scale MGs is developed,aiming to minimize the total operational cost and maximizeindividual benefits simultaneously.2) In each individual MG, the local EMS is designed basedon the detailed modeling of various energy resources includingPVs, ESs, EVs and dispatchable loads to decide optimalpower dispatches for the operational cost minimization. Atthe community level, a novel pairing algorithm is proposed toexplicitly find appropriate MG pairings with power surplus anddeficit. Based on the local scheduling in prior, the community-level EMS employs the pairing algorithm to settle specificpower exchanges among MGs, minimizing the total energytransactions with the upstream grid. The individual operationalcost is further reduced by additional economic benefits pro-cured by the community-level EMS.3) The proposed EMS has distinguished advantages onmodeling generality, computational efficiency and privacy pro-tection: a) Each local optimization problem is formulated as amixed-integer linear program (MILP), which can be solvedby using existing free/commercial solvers in parallel; b) Computational speed is improved significantly by thenon-iterative coordination strategy; and c) No information exchange among local EMSs is required,and communications between the community-level EMS andlocal EMSs only involve total energy exchanged with indi-vidual MGs. Therefore, private information such as detailedscheduling in MGs is well preserved.The remainder of this paper is organized as follows. InSection II, the overall system structure is presented. The math-ematical optimization model of individual MGs is formulatedin Section III. Section IV elaborates the pairing algorithmin the community-level EMS and the overall coordinationstrategy of the MG community. Case studies and simulationresults are discussed in Section V, in which the proposedEMS is simulated and compared with several benchmarkapproaches. At last, Section VI summarizes the conclusionof this paper and the future work is presented.II. S
TRUCTURE OF M ICROGRID C OMMUNITY
The coordinated control and communication architecture ofthe MG community considered in the study is schematicallyillustrated in Fig. 1. It is described as a small regionaldistributed power system comprising a community-level EMSand multiple MGs sited on different locations. The MGs areconnected with the transformer to the upstream grid througha common AC bus. The point where all the MGs and thetransformer have a common connection is regarded as thePCC. Each MG is locally equipped with PV, ES, EV anddifferent types of loads. The generalized model can be easily
Fig. 1. Network topology of a regional MG community. modified and utilized by changing these components to specifydifferent system frameworks, e.g. building clusters, residentialareas, etc.It is seen from Fig. 1 that the internal operation of eachindividual MG are supervised by the local EMS, which onlyneed to satisfy its self-interest. The MG-level EMSs optimizethe power scheduling for local controllable units, such asminimization of the operational cost. Microgrids can alsosell excess electricity back to the grid when the bidirectionaltransaction is allowed. On the other side, the community-levelEMS aims to manage the operation optimally for the entirecommunity by coordinating individual MGs, so that powerefficiency and economic benefits for both individual MGs andthe community are maximized simultaneously. To this extent,cyber communication is required by interaction between EMSsin different scales.The dynamic electricity price is determined usually by thesystem operator from the upstream grid. It is sensitive tolocational marginal prices and often announced hours ahead,allowing the decision makers to decide the power setpoints inadvance. For all the MGs connected to the PCC, the sameprice scheme should be received since they are physicallyconnected to the same bus. Typically, there is a differenceon the purchasing and selling price at each time period toprevent economic arbitrage. However, concerning on the self-operation status, some MGs may sell excessive electricity backto the grid while some others may purchase to offset energydeficits. For the entire MG community, this phenomenonwould lead to an undesirable result in terms of both power andeconomy efficiency. Frequent transactions between the MGcommunity and the upstream grid would introduce additionalpower transmission losses; on the other hand, uneconomicoperation of the MG community would become an issue dueto buying and selling price differences.To address the problems, the proposed EMS aims to min-imize energy transactions with the upstream grid such thatpower efficiency and economic benefits for both individualMGs and the entire community are maximized simultaneously.Details of the proposed hierarchically coordinated EMS willbe elaborated in Section III and IV.
Fig. 2. Piecewise linearized degradation cost of ES.
III. L
OCAL
EMS IN I NDIVIDUAL M ICROGRID
As a self-interested entity, the EMS in each individualMG aims to determine the optimal scheduling for the localoperational cost minimization. It collects all the informationincluding cost functions and various constraints of local facil-ities and determines input references of the control systemswithin a finite scheduling time.
A. Objective Function
Without loss of generality, the individual objective functioncan be formulated as follows: min ∑︁ 𝑡 ∈ 𝑇 𝑝 𝑖,𝑡𝑀,𝑏 𝑐 𝑡𝑏 Δ 𝑡 + 𝑝 𝑖,𝑡𝑀,𝑠 𝑐 𝑡𝑠 Δ 𝑡 + (cid:205) 𝑗 ∈{ 𝑵 𝑮 − 𝑖 } ( 𝑝 𝑖 𝑗,𝑡𝐶,𝑏 + 𝑝 𝑖 𝑗,𝑡𝐶,𝑠 ) 𝑐 𝑡𝐶 Δ 𝑡 + (cid:205) 𝑘 ∈ 𝐸𝑆 𝑖 𝑓 𝑘 [( 𝑝 𝑖,𝑡𝑘,𝑏 − 𝜁 𝑖𝑘 𝑝 𝑖,𝑡𝑘,𝑠 ) Δ 𝑡 ] , 𝑖 ∈ 𝑵 𝑮 (1)Each local EMS aims to minimize the operational costwithin the time 𝑻 , which depends on its own operationalrequirements and is not necessarily correspondent with thecommunity-level EMS. Investment costs of controllable ap-pliances such as EV and PV are not considered, since theproposed method is focused on operational optimization whereinvestment planning is out of this work’s scope.The first row in (1) represents the electricity cost withthe upstream grid. The time-varying dynamic pricing schemeprovides economic incentives by bilateral transaction, in whichthe purchasing price 𝑐 𝑡𝑏 is usually higher than the selling price 𝑐 𝑡𝑠 to prevent energy arbitrage. The second row represents thetransaction cost by power exchanges in the community, inwhich the transaction price 𝑐 𝑡𝐶 is predefined as the averageof 𝑐 𝑡𝑏 and 𝑐 𝑡𝑠 . The last row represents the degradation costassociated with ES. It is known that the degradation process ofES is nonlinearly related with its lifetime and operation mode[23]. To take the degradation cost in a practical fashion, thelinearized model is defined from its nonlinear form in [24] byusing inclining blocks, as shown in Fig. 2. The ES degradationcost 𝑓 𝑘 with special ordered set of type 2 (SOS-2) constraintscan be written as follows: 𝑓 𝑘 ( 𝑔 𝑖,𝑡𝑘 ) = ∑︁ 𝑛 ∈ 𝑵 𝒊𝒌 𝛼 𝑖,𝑡𝑘,𝑛 𝐹 ( 𝐺 𝑖𝑘,𝑛 ) (2) 𝑔 𝑖,𝑡𝑘 = ( 𝑝 𝑖,𝑡𝑘,𝑏 − 𝜁 𝑖𝑘 𝑝 𝑖,𝑡𝑘,𝑠 ) Δ 𝑡 = ∑︁ 𝑛 ∈ 𝑵 𝒊𝒌 𝛼 𝑖,𝑡𝑘,𝑛 𝐺 𝑖𝑘,𝑛 (3) ∑︁ 𝑛 ∈ 𝑵 𝒊𝒌 𝛼 𝑖,𝑡𝑘,𝑛 = , 𝛼 𝑖,𝑡𝑘 ∈ [ , ] (4) 𝐹 ( 𝐺 𝑖𝑘,𝑛 ) = 𝐹 ( 𝐺 𝑖𝑘,𝑛 − )+ 𝑐 𝑖𝑘,𝑛 − ( 𝐺 𝑖𝑘,𝑛 − 𝐺 𝑖𝑘,𝑛 − ) , 𝑛 ∈ 𝑵 𝒊𝒌 \{ } (5) 𝐹 ( 𝐺 𝑖𝑘, ) = (6)where 𝛼 𝑖,𝑡𝑘,𝑛 is the element of 𝑘 th ES in 𝑵 𝒊𝒌 that only theadjacent elements are nonzero. 𝑐 𝑖𝑘,𝑛 is the degradation costcoefficient of 𝑘 th ES, and 𝐺 𝑖𝑘,𝑛 is the power level at 𝑐 𝑖𝑘,𝑛 . B. Constraints
The objective function (1) is subject to the various con-straints on power balance, energy exchange, ES, EV and loads.
1) Power Balance
The total supply and demand must be always balancedwhich can be written as follows: 𝑝 𝑖,𝑡𝑀,𝑏 + 𝑝 𝑖,𝑡𝑀,𝑠 + 𝑝 𝑖,𝑡𝑃𝑉 + (cid:205) 𝑗 ∈{ 𝑵 𝑮 − 𝑖 } ( 𝑝 𝑖 𝑗,𝑡𝐶,𝑏 + 𝑝 𝑖 𝑗,𝑡𝐶,𝑠 )+ (cid:205) 𝑘 ∈ 𝑬𝑺 𝒊 ( 𝜁 𝑖𝑘 𝑝 𝑖,𝑡𝑘,𝑏 + 𝑝 𝑖,𝑡𝑘,𝑠 ) + (cid:205) 𝑘 ∈ 𝑬𝑽 𝒊 ( 𝜁 𝑖𝑘 𝑝 𝑖,𝑡𝑘,𝑏 + 𝑝 𝑖,𝑡𝑘,𝑠 ) = 𝑝 𝑖,𝑡𝐿 + (cid:205) 𝑘 ∈ 𝑳 𝒊 𝑝 𝑖,𝑡𝑘 𝜆 𝑖,𝑡𝑘 + (cid:205) 𝑘 ∈ 𝑳 𝒊 𝑝 𝑖,𝑡𝑘 𝜆 𝑖,𝑡𝑘 (7)The left side in (7) includes purchasing and selling power ofthe upstream grid, PV power output, transmitted power withother MGs, power of ES and power of EV. The right sideincludes variables composing three types of loads.
2) Power Exchange
The constraints include power exchange variables to theupstream grid and to other MGs as follows, respectively: ≤ 𝑝 𝑖,𝑡𝑀,𝑏 ≤ 𝑝 𝑖𝑀 𝑢 𝑖,𝑡𝑀 , 𝑡 ∈ 𝑻 (8) 𝑝 𝑖𝑀 ( − 𝑢 𝑖,𝑡𝑀 ) ≤ 𝑝 𝑖,𝑡𝑀,𝑠 ≤ , 𝑡 ∈ 𝑻 (9) ≤ 𝑝 𝑖 𝑗,𝑡𝐶,𝑏 ≤ 𝑝 𝑖 𝑗𝐶 𝑢 𝑖 𝑗,𝑡𝐶 , 𝑡 ∈ 𝑻 , 𝑗 ∈ 𝑵 𝑮 \{ 𝑖 } (10) 𝑝 𝑖 𝑗𝐶 ( − 𝑢 𝑖 𝑗,𝑡𝐶 ) ≤ 𝑝 𝑖 𝑗,𝑡𝐶,𝑠 ≤ , 𝑡 ∈ 𝑻 , 𝑗 ∈ 𝑵 𝑮 \{ 𝑖 } (11)where binary variables 𝑢 𝑖,𝑡𝑀 and 𝑢 𝑖 𝑗,𝑡𝐶 enforce the unidirectionalpower exchange at each time interval.
3) ES and EV
Constraints for ES are presented as follows: 𝐸 𝑖,𝑡 + 𝑘 = 𝐸 𝑖,𝑡𝑘 − 𝑝 𝑖,𝑡𝑘,𝑏 Δ 𝑡 − 𝜁 𝑖𝑘 𝑝 𝑖,𝑡𝑘,𝑠 Δ 𝑡, 𝑡 ∈ 𝑻 , 𝑘 ∈ 𝑬𝑺 𝒊 (12) 𝐸 𝑖𝑘 ≤ 𝐸 𝑖,𝑡𝑘 ≤ 𝐸 𝑖𝑘 , 𝑡 ∈ 𝑻 , 𝑘 ∈ 𝑬𝑺 𝒊 (13) ≤ 𝑝 𝑖,𝑡𝑘,𝑏 ≤ 𝑝 𝑖,𝑡𝑘 𝛿 𝑖,𝑡𝑘 , 𝑡 ∈ 𝑻 , 𝑘 ∈ 𝑬𝑺 𝒊 (14) 𝑝 𝑖,𝑡𝑘 ( − 𝛿 𝑖,𝑡𝑘 ) ≤ 𝑝 𝑖,𝑡𝑘,𝑠 ≤ , 𝑡 ∈ 𝑻 , 𝑘 ∈ 𝑬𝑺 𝒊 (15)(12)-(15) states the state dynamic, energy limits and powerlimits for ES, respectively.Constraints for EV are similarly described as follows: 𝐸 𝑖,𝑡 + 𝑘 = 𝐸 𝑖,𝑡𝑘 − 𝑝 𝑖,𝑡𝑘,𝑏 Δ 𝑡 − 𝜁 𝑖𝑘 𝑝 𝑖,𝑡𝑘,𝑠 Δ 𝑡, 𝑡 ∈ 𝑻 𝒊𝒌 , 𝑘 ∈ 𝑬𝑽 𝒊 (16) 𝐸 𝑖𝑘 ≤ 𝐸 𝑖,𝑡𝑘 ≤ 𝐸 𝑖𝑘 , 𝑡 ∈ 𝑻 𝒊𝒌 , 𝑘 ∈ 𝑬𝑽 𝒊 (17) ≤ 𝑝 𝑖,𝑡𝑘,𝑏 ≤ 𝑝 𝑖,𝑡𝑘 𝜃 𝑖,𝑡𝑘 , 𝑡 ∈ 𝑻 𝒊𝒌 , 𝑘 ∈ 𝑬𝑽 𝒊 (18) 𝑝 𝑖,𝑡𝑘 ( − 𝜃 𝑖,𝑡𝑘 ) ≤ 𝑝 𝑖,𝑡𝑘,𝑠 ≤ , 𝑡 ∈ 𝑻 𝒊𝒌 , 𝑘 ∈ 𝑬𝑽 𝒊 (19) 𝐸 𝑖,𝑡𝑘 ≥ 𝐸 𝑖,𝑑𝑒𝑝𝑘 , 𝑡 = 𝑇 𝑖𝑘 , 𝑘 ∈ 𝑬𝑽 𝒊 (20) Differently, the parking time is denoted by 𝑻 𝒊𝒌 that EV can bescheduled only when parked in MGs. Besides, (20) imposesthe minimum energy requirement at departure.
4) Loads
Loads are classified into non-dispatchable and dispatchableloads. Non-dispatchable loads represent fixed electricity con-sumption that cannot be shifted over time, which are modeledas an aggregated time-dependent parameter 𝑝 𝑖,𝑡𝐿 . Dispatchableloads represent electrical appliances which can be flexiblyscheduled. Based on different operation modes, two types ofdispatchable loads are defined. Type 1 loads can be dispatchedto several nonconsecutive time intervals, such as washingmachines that can do the wash and spin processes in differenttime periods. They are formulated as follows: ∑︁ 𝑡 ∈ 𝑻 𝑝 𝑖,𝑡𝑘 𝜆 𝑖,𝑡𝑘 Δ 𝑡 = 𝑃 𝑖,𝑡𝑘 , 𝑘 ∈ 𝑳 𝒊 (21) ∑︁ 𝑡 ∈ 𝑻 𝜆 𝑖,𝑡𝑘 = 𝐻 𝑖𝑘 , 𝑘 ∈ 𝑳 𝒊 (22)where (21) indicates the scheduled operation must meet totalenergy requirement, and (22) imposes the non-consecutiveoperational time constraint with the binary variable 𝜆 𝑖,𝑡𝑘 in-dicating operational status and the total duration 𝐻 𝑖𝑘 .Type 2 loads represent appliances such as toasters anddishwashers that must be scheduled consecutively. Their con-straints are modeled as follows: ∑︁ 𝑡 ∈ 𝑻 𝑝 𝑖,𝑡𝑘 𝜇 𝑖,𝑡𝑘 Δ 𝑡 = 𝑃 𝑖,𝑡𝑘 , 𝑘 ∈ 𝑳 𝒊 (23) ∑︁ 𝑡 ∈ 𝑻 𝜇 𝑖,𝑡𝑘 = 𝐻 𝑖𝑘 , 𝑘 ∈ 𝑳 𝒊 (24) ∑︁ 𝑡 ∈{ 𝑻 − 𝑇 } 𝜈 𝑖,𝑡𝑘,𝑠 = , 𝜈 𝑖,𝑡𝑘,𝑠 ∈ { , } , 𝑘 ∈ 𝑳 𝒊 (25) ∑︁ 𝑡 ∈{ 𝑻 − 𝑇 } 𝜈 𝑖,𝑡𝑘,𝑒 = − , 𝜈 𝑖,𝑡𝑘,𝑒 ∈ { , − } , 𝑘 ∈ 𝑳 𝒊 (26) 𝜇 𝑖,𝑡 + 𝑘 − 𝜇 𝑖,𝑡𝑘 = 𝜈 𝑖,𝑡𝑘,𝑠 + 𝜈 𝑖,𝑡𝑘,𝑒 , 𝑡 ∈ { 𝑻 − 𝑇 } , 𝑘 ∈ 𝑳 𝒊 (27)where (25)-(27) are additionally imposed with integral vari-ables { 𝜈 𝑖,𝑡𝑘,𝑠 , 𝜈 𝑖,𝑡𝑘,𝑒 } indicating starting and ending time toaddress the consecutive operation feature. C. Overall Formulation
Each individual optimization problem 𝑴 𝒊 for MG 𝑖 can bedescribed as follows: 𝑴 𝒊 : for 𝑖 ∈ 𝑵 𝑮 : min : (1) subject to : (2) − (27) 𝑴 𝒊 is formulated as a MILP which can be effectively solvedby many open-source and commercial solvers.IV. C ENTRAL
EMS IN M ICROGRID C OMMUNITY
The community-level EMS aims to determine a pricingmechanism of settling transactions for MGs to further reducetheir operating costs. It allocates internal power exchangesamong MGs to minimize the energy transactions with theupstream grid. In this section, a pairing algorithm is pro-posed to explicitly find the MG pairings with least power transmission distances, equivalently to minimize power lossesand energy transactions. The coordination strategy is presentedto determine specific power exchanges among MGs withsurplus and deficit so that the transmission loss is equivalentlyminimized. Consequently, the individual operational cost isfurther reduced by additional economic benefits procured bythe community-level EMS.
A. Pairing Algorithm
The pairing algorithm identifies each distinct pair of MGswith minimal power transmission losses, so that the pat-tern of exchanging energy inside the MG community canbe established. To achieve this target, appropriate weightingcoefficients need to be addressed to determine the pairingpriority. Since the MG community is particularly regional,electrical distances of MGs are considered to be so closethat specific line resistance parameters may not be attainedexplicitly [25], [26]. Therefore, geographical distances areused instead as weighting coefficients to indirectly reflecttransmission losses induced by power exchange among MGs,since they are approximately proportional to line resistanceswithin small regions [27], [28]. The loss factor coefficient 𝜀 𝑖 𝑗 is specified as well to present the linear transmission loss ina practical fashion.Accordingly, a 2-D Cartesian coordinate system is formu-lated where the location of MG 𝑖 is expressed by its geographi-cal coordinates ( 𝑙 𝑥𝑖 , 𝑙 𝑦𝑖 ) . Hence, the weighting coefficient 𝑤 𝑖 𝑗 ofMGs { 𝑖, 𝑗 } representing the transmission loss can be expressedby their Euclidean distance as follows: 𝑤 𝑖 𝑗 = 𝜀 𝑖 𝑗 √︃ ( 𝑙 𝑥𝑖 − 𝑙 𝑥𝑗 ) + ( 𝑙 𝑦𝑖 − 𝑙 𝑦𝑗 ) , 𝑖 ≠ 𝑗, 𝑖, 𝑗 ∈ 𝑵 𝑮 (28)Note that 𝑤 𝑖 𝑗 for MGs with no physical connection can be setas a large positive number 𝑀 , and intuitively, 𝑤 𝑖𝑖 = 𝑀, 𝑖 ∈ 𝑵 𝑮 as no self connection exists. The weighting matrix 𝑊 of theentire community is expressed as follows: 𝑊 = 𝑤 𝑤 · · · 𝑤 𝑁 𝑔 𝑤 𝑤 · · · 𝑤 𝑁 𝑔 ... ... . . . ...𝑤 𝑁 𝑔 𝑤 𝑁 𝑔 · · · 𝑤 𝑁 𝑔 𝑁 𝑔 (29)It can be easily recognized that 𝑊 is 𝑁 𝑔 × 𝑁 𝑔 symmetric.Each row 𝑟 𝑖 = { 𝑤 𝑖 𝑗 | 𝑗 ∈ 𝑵 𝑮 } in 𝑊 comprises the weightingcoefficients of MG 𝑖 to other MGs. Next, we prove thatthere always exists a pairing ( 𝑤 𝑖 𝑗 , 𝑤 𝑗𝑖 ) in 𝑊 for the MGcommunity set 𝑵 𝑮 , in which they are of minimal values intheir corresponding rows 𝑟 𝑖 and 𝑟 𝑗 . Theorem 1 (Pairing Algorithm) . A MG pairing with minimalweighting coefficients to their corresponding rows in 𝑊 canbe always found, provided that 𝑊 is symmetric.Proof of Theorem 1: We denote 𝑖, 𝑗 ∈ 𝑵 𝑮 to be the indicesof corresponding rows and columns in 𝑊 , respectively. Theminimum in each row 𝑟 𝑖 , 𝑤 𝑖 , can be expressed as follows: 𝑤 𝑖 = min 𝑟 𝑖 = min 𝑗 ∈ 𝑵 𝑮 𝑤 𝑖 𝑗 , 𝑖 ∈ 𝑵 𝑮 (30) The set 𝑹 including all 𝑤 𝑖 can be further presented as: 𝑹 = { 𝑤 𝑖 | 𝑤 𝑖 = min 𝑗 ∈ 𝑵 𝑮 𝑤 𝑖 𝑗 , 𝑖 ∈ 𝑵 𝑮 } = { 𝑤 𝑖𝑐 𝑖 | 𝑤 𝑖𝑐 𝑖 = min 𝑗 ∈ 𝑵 𝑮 𝑤 𝑖 𝑗 , 𝑖 ∈ 𝑵 𝑮 } (31)where 𝑪 = { 𝑐 𝑖 | 𝑖 ∈ 𝑵 𝑮 } is the column index set of minimumelements.To prove by contradiction, we make its opposite proposition that such a pairing does not exist for all MGs in 𝑵 𝑮 . Thisopposite proposition implies that 𝑐 𝑖 ∈ 𝑪 are all different since 𝑤 𝑖 ∈ 𝑹 are all different.For symbol simplification, we denote the index set 𝑲 as 𝑲 = { 𝑘 𝑖 ∈ 𝑪 | 𝑘 = , · · · , 𝑘 𝑖 = 𝑐 𝑘 𝑖 − , 𝑖 ∈ 𝑵 𝑮 } (32)Since 𝑊 is symmetric, in 𝑘 th row, we have: 𝑤 𝑐 = 𝑤 𝑘 𝑐 𝑘 = 𝑤 𝑐 𝑘 𝑘 = 𝑤 𝑘 𝑘 (33)It is known from (32) that 𝑤 𝑘 𝑐 𝑘 is the minimum in the 𝑘 throw and 𝑘 ≠ 𝑐 𝑘 . Therefore, we have: 𝑤 𝑘 𝑘 > 𝑤 𝑘 𝑐 𝑘 = 𝑤 𝑐 𝑘 𝑘 = 𝑤 𝑘 𝑘 (34)Sequentially for 𝑘 ∈ 𝑲 , the following formation must satisfy: 𝑤 𝑘 𝑐 𝑘 > 𝑤 𝑘 𝑐 𝑘 > · · · > 𝑤 𝑘 𝑁𝑔 − 𝑐 𝑘𝑁𝑔 − = 𝑤 𝑘 𝑁𝑔 𝑘 𝑁𝑔 − (35)For the last element 𝑤 𝑘 𝑁𝑔 𝑘 𝑁𝑔 − , we can get: 𝑤 𝑘 𝑁𝑔 𝑘 𝑁𝑔 − > 𝑤 𝑘 𝑁𝑔 𝑐 𝑘𝑁𝑔 (36)Recall that 𝑐 𝑖 ∈ 𝑪 are all different, 𝑘 ∈ 𝑲 \{ 𝑘 𝑁 𝑔 } are alsoall different. However, since 𝑊 is a 𝑁 𝑔 × 𝑁 𝑔 matrix, 𝑲 musthave exactly 𝑁 𝑔 elements. Therefore, the following formationmust satisfy: 𝑲 \{ 𝑘 𝑁 𝑔 } = 𝑲 (37)(37) means 𝑤 𝑘 𝑁𝑔 𝑐 𝑘𝑁𝑔 is equal to at least one element in theminimum row set 𝑹 : 𝑤 𝑘 𝑁𝑔 𝑐 𝑘𝑁𝑔 ∈ 𝑅, 𝑘 𝑁 𝑔 ∈ 𝑲 \{ 𝑘 𝑁 𝑔 } (38)(38) is contradictory to the opposite proposition . Hence, itis proved that such the pairing with minimal values for 𝑊 canbe always found.By removing invalid pairings whose connections are notconstructed and self-pairings in prior, it is straightforward todetermine the MG pairings with minimal transmission lossesin the community by using the pairing algorithm. Accordingly,after the minimal value of rows in 𝑊 is found, the pairing 𝑥, 𝑦 ∈ 𝑵 𝑮 for 𝑊 can be determined by looking into the samevalues of these minimums as follows: { 𝑥, 𝑦 } = { 𝑖, 𝑗 }|{ 𝑤 𝑖 𝑗 = 𝑤 𝑗𝑖 , 𝑤 𝑖 𝑗 ∈ 𝑹 , 𝑖, 𝑗 ∈ 𝑵 𝑮 } (39) 𝑝 𝑥𝑦,𝑡𝐶,𝑏 = 𝑝 𝑥,𝑡𝐶 , 𝑝 𝑥𝑦,𝑡𝐶,𝑠 = , 𝑝 𝑦𝑥,𝑡𝐶,𝑏 = , 𝑝 𝑦𝑥,𝑡𝐶,𝑠 = − 𝑝 𝑥,𝑡𝐶 /( − 𝑤 𝑥𝑦 ) , if 𝑝 𝑥,𝑡𝐶 > , | 𝑝 𝑥,𝑡𝐶 | < |( − 𝑤 𝑥𝑦 ) 𝑝 𝑦,𝑡𝐶 | 𝑝 𝑥𝑦,𝑡𝐶,𝑏 = −( − 𝑤 𝑥𝑦 ) 𝑝 𝑦,𝑡𝐶 , 𝑝 𝑥𝑦,𝑡𝐶,𝑠 = , 𝑝 𝑦𝑥,𝑡𝐶,𝑏 = , 𝑝 𝑦𝑥,𝑡𝐶,𝑠 = 𝑝 𝑦,𝑡𝐶 , if 𝑝 𝑥,𝑡𝐶 > , | 𝑝 𝑥,𝑡𝐶 | > |( − 𝑤 𝑥𝑦 ) 𝑝 𝑦,𝑡𝐶 | 𝑝 𝑥𝑦,𝑡𝐶,𝑏 = , 𝑝 𝑥𝑦,𝑡𝐶,𝑠 = 𝑝 𝑥,𝑡𝐶 , 𝑝 𝑦𝑥,𝑡𝐶,𝑏 = −( − 𝑤 𝑥𝑦 ) 𝑝 𝑥,𝑡𝐶 , 𝑝 𝑦𝑥,𝑡𝐶,𝑠 = , if 𝑝 𝑥,𝑡𝐶 < , |( − 𝑤 𝑥𝑦 ) 𝑝 𝑥,𝑡𝐶 | < | 𝑝 𝑦,𝑡𝐶 | 𝑝 𝑥𝑦,𝑡𝐶,𝑏 = , 𝑝 𝑥𝑦,𝑡𝐶,𝑠 = − 𝑝 𝑦,𝑡𝐶 /( − 𝑤 𝑥𝑦 ) , 𝑝 𝑦𝑥,𝑡𝐶,𝑏 = 𝑝 𝑦,𝑡𝐶 , 𝑝 𝑦𝑥,𝑡𝐶,𝑠 = , if 𝑝 𝑥,𝑡𝐶 < , |( − 𝑤 𝑥𝑦 ) 𝑝 𝑥,𝑡𝐶 | > | 𝑝 𝑦,𝑡𝐶 | , 𝑡 ∈ 𝑻 (42) 𝑝 𝑥,𝑡𝐶 = , 𝑝 𝑦,𝑡𝐶 = 𝑝 𝑦,𝑡𝐶 + 𝑝 𝑥,𝑡𝐶 /( − 𝑤 𝑥𝑦 ) , if 𝑝 𝑥,𝑡𝐶 > , | 𝑝 𝑥,𝑡𝐶 | < |( − 𝑤 𝑥𝑦 ) 𝑝 𝑦,𝑡𝐶 | 𝑝 𝑦,𝑡𝐶 = 𝑝 𝑥,𝑡𝐶 + ( − 𝑤 𝑥𝑦 ) 𝑝 𝑦,𝑡𝐶 , 𝑝 𝑥,𝑡𝐶 = , if 𝑝 𝑥,𝑡𝐶 > , | 𝑝 𝑥,𝑡𝐶 | > |( − 𝑤 𝑥𝑦 ) 𝑝 𝑦,𝑡𝐶 | 𝑝 𝑥,𝑡𝐶 = , 𝑝 𝑦,𝑡𝐶 = 𝑝 𝑦,𝑡𝐶 + ( − 𝑤 𝑥𝑦 ) 𝑝 𝑥,𝑡𝐶 , if 𝑝 𝑥,𝑡𝐶 < , |( − 𝑤 𝑥𝑦 ) 𝑝 𝑥,𝑡𝐶 | < | 𝑝 𝑦,𝑡𝐶 | 𝑝 𝑦,𝑡𝐶 = 𝑝 𝑥,𝑡𝐶 + 𝑝 𝑦,𝑡𝐶 /( − 𝑤 𝑥𝑦 ) , 𝑝 𝑥,𝑡𝐶 = , if 𝑝 𝑥,𝑡𝐶 < , |( − 𝑤 𝑥𝑦 ) 𝑝 𝑥,𝑡𝐶 | > | 𝑝 𝑦,𝑡𝐶 | , 𝑡 ∈ 𝑻 (43) B. Coordination Strategy in Microgrid Community
The pairing algorithm has demonstrated MG pairings withminimal transmission loss can be always located for theentire community. However, such a pairing is regarded validbetween two MGs only with different power flow directions.To this extent, the coordination strategy recognizes all the validpairings of MGs with power surplus and deficits, determinesspecific values for corresponding energy transactions andsimultaneously minimizes the total transaction loss in the MGcommunity. To reach this target, total transmitted power ofindividual MGs with respect to the community need to befirstly distinguished. An auxiliary variable 𝑝 𝑖,𝑡𝐶 for 𝑖 th MG isintroduced as follows: 𝑝 𝑖,𝑡𝐶 = 𝑝 𝑖,𝑡𝑀,𝑏 + 𝑝 𝑖,𝑡𝑀,𝑠 + ∑︁ 𝑗 ∈ 𝑵 𝑮 \{ 𝑖 } ( 𝑝 𝑖 𝑗,𝑡𝐶,𝑏 + 𝑝 𝑖 𝑗,𝑡𝐶,𝑠 ) , 𝑡 ∈ 𝑻 (40)where 𝑝 𝑖,𝑡𝐶 is the summed transmitted power of 𝑖 th MG to allother MGs in 𝑵 𝑮 and the upstream grid.It is recognized that 𝑝 𝑖,𝑡𝐶 is positive when the 𝑖 th MG haspower surplus and negative with power deficit. Based on thepower flow directions, therefore, the corresponding elementsin 𝑊 can be excluded by the signs of 𝑝 𝑖,𝑡𝐶 as follows: 𝑤 𝑖 𝑗 = 𝑀, if 𝑝 𝑖,𝑡𝐶 × 𝑝 𝑗,𝑡𝐶 ≥ , 𝑖, 𝑗 ∈ 𝑵 𝑮 (41)where 𝑀 is a large positive number.After elimination of irrelevant parameters, valid pairingsof MGs with different power flow directions can be alwaysestablished by using the modified coefficient matrix 𝑊 in(28), (29) and (41). Based on the optimized dispatch signalstransmitted from local EMSs, the community-level EMS candetermine the transactions among MGs explicitly.The community-level EMS executes the pairing algorithmto find MGs in a pairing with minimal weighting coefficients,marked as 𝑥, 𝑦 ∈ 𝑵 𝑮 . Correspondingly, the variables relatedto exchanged power of MGs 𝑥, 𝑦 need to be updated in theMG level. For all possible scenarios, the transmitted powerof MGs 𝑥, 𝑦 are defined by (42), and variables 𝑝 𝑥,𝑡𝐶 and 𝑝 𝑦,𝑡𝐶 indicating summed transmitted power of MGs 𝑥, 𝑦 respectivelyare updated by (43) as well.At last, the weighting matrix 𝑊 is updated as follows sothat the successfully paired MGs have been excluded: 𝑤 𝑖 𝑗 = 𝑀 ∀ 𝑤 𝑖 𝑗 ∈ 𝑟 𝑖 & 𝑗 ∈ 𝑵 𝑮 , if 𝑝 𝑖,𝑡𝐶 = , 𝑖 ∈ { 𝑥, 𝑦 } (44)(44) finishes the first MG pairing, and the community-levelEMS starts searching next pairing for the rest of MGs, until for 𝑡 ∈ 𝑻 , do Lower-level EMS for individual MGs: for MG 𝑖 ∈ 𝑵 𝑮 , do
1. Make local PV, load and electricity price forecast in 𝑻 .
2. Solve the local optimization problem 𝑴 𝒊 .
3. Determine the decision variables { 𝑝 𝑖,𝑡𝑘,𝑏 , 𝑝 𝑖,𝑡𝑘,𝑠 , 𝑢 𝑖,𝑡𝑀 , 𝛿 𝑖,𝑡𝑘 , 𝜃 𝑖,𝑡𝑘 , 𝜆 𝑖,𝑡𝑘 , 𝜇 𝑖,𝑡𝑘 , 𝜈 𝑖,𝑡𝑘,𝑠 , 𝜈 𝑖,𝑡𝑘,𝑒 , 𝛼 𝑖,𝑡𝑘,𝑛 } and { 𝑢 𝑖,𝑡𝑀 , 𝑢 𝑖 𝑗,𝑡𝐶 } .
4. Aggregate 𝑝 𝑖,𝑡𝑐 according to (40), and transfer { 𝑝 𝑖,𝑡𝑀,𝑏 ,𝑝 𝑖,𝑡𝑀,𝑠 , 𝑝 𝑖 𝑗,𝑡𝐶,𝑏 , 𝑝 𝑖 𝑗,𝑡𝐶,𝑠 } to be decided by the community-levelEMS. end for Community-level EMS for MG community:
1) Formulate the weighting matrix 𝑊 according to (28), (29)and (41). while (45) is met, do
2) Find the minimum of each row in 𝑊 , and determine thespecific pairing { 𝑥, 𝑦 } with the same smallest coefficientsaccording to Theorem 1 and (39).
3) Update { 𝑝 𝑖 𝑗,𝑡𝑐,𝑏 , 𝑝 𝑖 𝑗,𝑡𝑐,𝑠 } , 𝑖, 𝑗 ∈ 𝑵 𝑮 by (42).
4) Update aggregated power variables 𝑝 𝑖,𝑡𝐶 ,𝑖 ∈ 𝑵 𝑮 by (43).
5) Update the weighting matrix 𝑊 by (44). end while
6) Determine the power exchange variables { 𝑝 𝑖,𝑡𝑀,𝑏 , 𝑝 𝑖,𝑡𝑀,𝑠 , 𝑝 𝑖 𝑗,𝑡𝐶,𝑏 , 𝑝 𝑖 𝑗,𝑡𝐶,𝑠 } , 𝑖 ∈ 𝑵 𝑮 . end for Fig. 3. Algorithm of the hierarchically coordinated EMS. any of the total energy surplus of deficit among 𝑵 𝑮 becomeszero. The stopping criterion can be expressed as follows: ∑︁ 𝑖 ∈ 𝑵 𝑮 ∑︁ 𝑗 ∈{ 𝑵 𝑮 − 𝑖 } 𝑝 𝑖 𝑗,𝑡𝐶,𝑏 × ∑︁ 𝑖 ∈ 𝑵 𝑮 ∑︁ 𝑗 ∈{ 𝑵 𝑮 − 𝑖 } 𝑝 𝑖 𝑗,𝑡𝐶,𝑠 = (45)The overall procedure of the proposed EMS is describedin Fig. 3. In the beginning of each time period, PV and loadforecasts are made locally and the day-ahead electricity priceis obtained. For each MG 𝑖 ∈ 𝑵 𝑮 , dispatch decisions in theentire scheduling horizon are obtained by solving its ownoptimization problem in the local EMS individually, and 𝑝 𝑖,𝑡𝐶 is calculated by (40). Then for the community-level EMS, 𝑊 is re-established based on (28), (29) and (41). Afterwards, thecommunity-level EMS finds the MG pairing for current 𝑊 .Procedures of the coordination strategy in the community-levelEMS are iterated by (40)–(44) until (45) is met. C. Remarks
It is worth mentioning that the proposed pairing algorithmis not to physically control the power flow from one MGto the other. Rather, it is to settle the energy transactionswithin different MGs in a hierarchical way. Specifically, thelocal EMS determines the optimal power dispatch for eachindividual MG, and all the excessive power will go to the PCCfor power exchange. The pairings of power surplus and deficitare then established based on the in-prior local scheduling inthe community-level EMS. In this way, each MG can transactwith others rather than the upstream grid to save the operatingcost. It is important to note that the community-level EMS isnot to physically dispatch the power but to settle the energytransactions, and the power surplus and deficit of all theindividual MGs are balanced with the upstream grid at thePCC. Also note in Fig. 3 that the community-level EMS has noiterative information exchange with the local EMS since 𝑝 𝑖,𝑡𝐶 isonly collected once from the corresponding 𝑖 th local EMS, andthat the local EMS can solve the MILP optimization problemin parallel. Such the non-iterative interaction and paralleloptimization will improve the computational speed of theproposed EMS over the existing techniques. The verificationon computation speed will be provided in Section V.On the selection of weighting coefficients, as the electricaldistances of MGs are close due to the regionally small area,it is usually not feasible to obtain exact line parametersand thus hard to calculate the explicit power losses. It issimilarly suggested in [29], [30] that the fixed R/X ratio canbe employed approximately in the homogeneous distributionsystem to calculate the line parameters. On the other hand,since it is only required in Theorem 1 that the weightingcoefficient matrix 𝑊 is symmetric, the specific line parameterscan be readily employed as weighting coefficients for theproposed algorithm without affecting its effectiveness if theyare explicitly known beforehand.V. S IMULATION R ESULTS
In this section, the mathematical model of the proposedEMS is demonstrated in MATLAB. The optimization problemis solved using Gurobi [31], in which the local EMS inindividual MG solves its own optimization. The community-level EMS settles the power exchanges among MGs by usingthe coordination strategy with pairing algorithm, so that thetotal power transactions with the upstream grid is minimized.The simulation is conducted for a 24h scheduling horizon, andthe sampling time resolution for the community-level EMS is0.5h.
A. Case 1: 4-MG Community
In this case study, a MG community with 4 differenttypes of MGs (MG1-MG4) is investigated. MG1 and MG2are considered as two individual houses with different loadpatterns. MG3 is an apartment building with 10 households.MG4 is a small-scale MG with high PV penetration, whereits renewable output is much larger than the total load. Thespecifications of 4 MGs are detailed in Table I. For eachhouseholds in individual houses and apartment, type 1 and type2 loads are listed in Table II with predefined operation timeranges. The PV profile is based on the solar radiation data from
TABLE IM
ICROGRID C HARACTERISTICS
Microgrid
MG1 MG2 MG3 MG4 ES Capacity(kWh) 8 8 12 12Max&Min 𝑃 (kW) -4/4 -4/4 -4/4 -4/4Initial SOC(%) 20.9 33.1 33 31SOC range(%) 17.0-84.1 17.5-83.5 16.9-82.1 18.7-89.0Efficiency 95% 95% 95% 95% EV Capacity (kWh) 16 16 N.A. N.A.Max&Min 𝑃 (kW) -1.44/3.6 -1.44/3.6Initial SOC(%) 52.63 33.1Operation periods (h) 0-4.88, 19.09-24 0-7.65,18.93-24SOC range(%) (%) 15.8-83.7 19.9-81.6Min depart SOC(%) 51.45 61.58Efficiency 95% 95% PV Capacity (kWp) 2 2 16 16
Unified location ( 𝑙 𝑥 ,𝑙 𝑦 ) (0.12, 0.13) (0.16, 0.79) (0.83, 0.11) (0.09, 0.26) TABLE IIP
ARAMETERS OF DISPATCHABLE LOADS
Appliance Power(kW) Operating Operation typeperiods duration(h)Washing machine 0.7 0-19,23-24 1 1Cleaner 0.6 0-4,6,24 4 1Air conditioner 1.2 0-7,18-24 3 1Lighting 0.15 6-7,18-23.5 5 1Oven 1.16 11-13 0.5 1Toaster 1.2 7-9 0.25 2Dish washer 1 0-4,9-11,14-17,20-24 1 2 (a) MG1 (b) MG2(c) MG3 (d) MG4Fig. 4. PV outputs of MGs.(a) MG1 (b) MG2(c) MG3 (d) MG4Fig. 5. Non-dispatchable loads of MGs.
Fig. 6. Electricity price in 24 hours. [32], which is depicted in Fig. 4. The non-dispatchable loadand electricity price data are based on the average householdstatistics in 2017 [33] and the hourly market data in Singapore[34], which are shown in Fig. 5 and Fig. 6, respectively.Specifically, to indicate different patterns, the load profile ofMG2 is shifted so that it has the peak power consumption inthe daytime. The loss factors in the community 𝜀 𝑖 𝑗 , 𝑖, 𝑗 ∈ 𝑵 𝑮 are set to be 0.05.
1) Results of Individual Microgrids
The hourly energy dispatch for MG1 and MG2 (houses)is presented in Fig. 7a and Fig. 7b. It is observed that MG1and MG2 can cover most of electricity demand themselves byPV during daytime. Dispatchable loads are scheduled withinoff-peak hours due to low electricity price. ES and EV arealso charged until the required energy levels are reached athours with low electricity prices (e.g., at hour 2 and 23).However, ES can effectively respond high price signals in thedaytime whereas EV is not involved as it is already departed.Particularly, when the electricity price increases at hour 7, EVin MG2 starts to charge to reduce electricity consumption ofthe upstream grid.The scheduling of appliances in MG1 is presented in Fig. 8for detailed illustration. Most power consumption is distributedamong time intervals when electricity prices are at lowesteven full scheduling flexibility is provided. On the other side,power consumption of type 2 loads is moved towards hourswith higher prices to meet users’ demands. For both types ofdispatchable loads, time intervals with lowest prices are alwaysselected by the local EMS.The scheduling for MG3 (apartment building) is shown inFig. 7c. Similarly, the load consumption is mostly distributedamong time intervals with low electricity price. Both types ofdispatchable loads are scheduled within off-peak hours eventhough type 1 loads have full flexibility during the entirehorizon. However, different from MG1 and MG2 (houses),it is necessary for MG3 to buy part of additional power fromother MGs with surplus or even from the upstream grid sincethe demand cannot be fully covered by its own PV output.The scheduling of MG4 is shown in Fig. 7d, in which thisMG owns small non-dispatchable loads. In consequence, thenet power is exported to other MGs. On the other hand, powerconsumption at night is supplied by the local energy storage,the upstream grid and other MGs together since PV is unableto provide any power.
2) Results of Microgrid community
The energy flow within the MG community is detailed inTable III, in which four MGs are abbreviated from 1 to 4,respectively. It is shown that MG1 has the higher priorityto export its surplus to MG3 due to a smaller weightingcoefficient, even when MG1 and MG2 have excessive power (a) MG1(b) MG2(c) MG3(d) MG4Fig. 7. Energy scheduling in different MGs.Fig. 8. Detailed scheduling of dispatchable loads in MG1. from the PV at daytime. Similarly, when the PV output inMG1 cannot meet all the local loads at hour 17, the higherpriority has granted it to acquire additional power from MG4than MG1 and MG2.With the implementation of the proposed method, the to-tal operational cost has been not only decreased for eachindividual MG, but for the entire community, as shown inTable IV. Compared with direct transaction with the upstreamgrid, the operational cost of each MG has been reducedfrom 5.109% to 21.544%. On the other hand, by using thecoordination strategy, the transaction cost with the upstreamgrid has been decreased by $8.231 even with additional $1.245of transmission loss. In consequence, the operational cost intotal has been decreased by 9.474%. Therefore, individualMGs can benefit from the proposed EMS by reducing localoperational costs, which would potentially attract externalMGs for active participation into the community.
TABLE IIIE
NERGY FLOW RESULTS IN HOURS
Time Energy flow (kWh)(h)
TABLE IVO
PERATION COST OF MG COMMUNITY WITH S Cost ($) MG1 MG2 MG3 MG4 totaloriginal 5.981 6.068 72.233 -10.558 73.724grid-side 5.496 5.036 56.028 -1.068 65.493community -0.075 0.560 12.513 -11.753 1.245total 5.421 5.596 68.542 -12.821 66.737improvement 9.361% 7.619% 5.109% 21.544% 9.474%
TABLE VA
VERAGE OPERATION COST OF COMMUNITY WITH
50 MG S Cost ($) MG1 MG2 MG3 MG4 totaloriginal 6.083 6.035 71.979 -10.487 548.361grid-side 5.503 5.040 55.770 -1.059 490.268community 0.208 0.560 12.306 -10.996 8.036total 5.711 5.600 68.076 -12.055 498.304improvement 6.111% 7.201% 5.422% 14.958% 9.129%
B. Case 2: 50-MG community
A regional MG community with 50 MGs in four typesincluding 20 of MG1, 20 of MG2, 5 of MG3 and 5 of MG4,respectively, is further investigated to validate the scalabilityof the proposed EMS. Individual MG characteristics followthose of same types in Case 1.The operational cost results are presented in Table V.It is observed the entire MG community has reduced theoperational cost in 24 hours from $548.361 to $490.268,while the total transmission loss is $8.036. In total, theelectricity expense has been improved by 9.129%. In addition,the proposed EMS benefits all types of individual MGs withaverage cost improvements ranging from 5.422% to 14.958%.As a result, the implementation of the proposed EMS may
TABLE VIC
OMPARATIVE RESULTS FOR S Algorithm Operational cost ($) Computation time (s)proposed 66.73 1.17[35] 66.60 36.16[22] 66.67 22.49direct transaction 73.72 1.01
TABLE VIIC
OMPARATIVE RESULTS FOR
50 MG S Algorithm Operational cost ($) Computation time (s)proposed 498.30 15.06[35] 497.22 2053.48[22] 497.96 1378.13direct transaction 617.41 12.82 implicitly decrease the electricity price from the upstream gridin turn, since the stress to power congestion at peak hours inthe distribution level would be alleviated.Comparing the result with that in the 4-MG case, it is notedthat the ratio of operational result reduction does not neces-sarily decrease with the increasing size of MG community,since it is closely related on the different MG types and theirindependent operational states, such as RES outputs, fixed anddispatchable load profiles, electricity prices and so on.
C. Comparison with Other Methods
Three existing approaches in the literature are conducted forcomparison to further evaluate the performance and advantagesof the proposed EMS. Firstly, the single-level energy manage-ment framework in [35] is adopted as the centralized bench-mark in which all the MGs in the community are combined justas one unity. A mathematical model similar in Section III-Bis formulated and solved. Secondly, the optimization methodproposed in [22] without stochastic processes is utilized in thecommunity level as the two-level EMS benchmark, in whicha Lagrangian relaxation based algorithm is used to eliminatepower exchange imbalances. Finally, a purely decentralizedframework by only using local EMSs is added in which eachMG makes transaction directly with the upstream grid, withoutany communication inside the community.Comparative results with existing methods in Case 1 and2 are presented in Table VI and Table VII, respectively. Itis seen in Table VI that the proposed EMS has achieved theoptimized operational cost slightly higher by just 0.2% to thebest result with [35], whereas the computation time is nearly19 times faster than the second best result with [22]. It is notedthat the operational cost in [35] is the minimum since all theinformation from individual MGs has been fully collected andgathered into the centralized EMS, which may neverthelessbring serious privacy concerns. Similar privacy problems existin [22] that information of dispatch signals needs to beexchanged among MGs and with the community-level EMS.On the contrary, private information is well preserved in theproposed EMS, since no communication among local EMSsor with the community-level EMS is required by any means.Communications between the community-level EMS and localEMSs only involve total power exchanges of individual MGsthat do not expose any detailed decision making inside MGs. The benefits on computational speed of the proposed EMSare further revealed with the increasing number of MGs, asshown in Table VII. It is seen that the proposed EMS spendsjust 15 seconds to the optimized result with a degradation of0.21%, however it takes nearly half an hour for the centralizedmethod in [35] and 23 minutes for the decentralized approachin [22]. Such the discrepancy on computational efficiencywould become more noticeable with size expansion of theMG community, therefore, the proposed EMS has outstand-ing advantages in view of trade-offs between computationefficiency and solution quality. With this respect, it is notedthat the uncertainty related with renewables and loads arenot modeled in the proposed method because of its superiorperformance on computation speed. The proposed EMS is ableto be carried out more frequently if uncertain factors are takeninto consideration. VI. C
ONCLUSION
A. Summary
In this paper, a hierarchically coordinated EMS modelfor multiple small-scale MGs in a regional community isproposed, accounting for minimization of the community-level operational cost and maximization of individual MG-level benefits simultaneously. The local EMSs aim to minimizethe individual operational cost, while the community-levelEMS determines specific energy transactions in the communityby using the pairing algorithm to further reduce individualoperational costs. The proposed EMS has been validated bytwo case studies with different scales. By comparing withexisting approaches, simulation results have shown significantadvantages of the proposed EMS on modeling generality,computational complexity and privacy security, that the op-timization time has been reduced significantly by the non-iterative algorithm, and privacy issues have been eliminatedby minimal information exchange.
B. Future work
There have been studies addressing uncertainties by im-plementing stochastic optimization techniques [36]–[38], inwhich uncertainties are usually handled by sampling reduc-tion and uncertainty set in stochastic programming, and thenthe optimization problems can be solved in multiple stages.Nevertheless, most of the techniques and algorithms men-tioned above have been implemented to the centralized energymanagement framework whereas little application has beenreported regarding decentralized energy management. In ourfuture research, it is planned to incorporate uncertainties intothe proposed model with distributed stochastic optimizationschemes, and develop computationally efficient algorithm forpractical application.A
CKNOWLEDGMENT
This research is supported by the National Research Foun-dation, Prime Minister’s Office, Singapore under the En-ergy Innovation Research Programme (EIRP) Energy StorageGrant Call and administrated by the Energy Market Authority(NRF2015EWT-EIRP002-007). R
EFERENCES[1] H. Kanchev, D. Lu, F. Colas, V. Lazarov, and B. Francois, “Energymanagement and operational planning of a microgrid with a pv-basedactive generator for smart grid applications,”
IEEE transactions onindustrial electronics , vol. 58, no. 10, pp. 4583–4592, 2011.[2] A. Anvari-Moghaddam, J. M. Guerrero, J. C. Vasquez, H. Monsef,and A. Rahimi-Kian, “Efficient energy management for a grid-tiedresidential microgrid,”
IET Generation, Transmission & Distribution ,vol. 11, no. 11, pp. 2752–2761, 2017.[3] N. Liu, Q. Chen, J. Liu, X. Lu, P. Li, J. Lei, and J. Zhang, “A heuristicoperation strategy for commercial building microgrids containing evsand pv system,”
IEEE Transactions on Industrial Electronics , vol. 62,no. 4, pp. 2560–2570, 2015.[4] X. Liu, P. Wang, and P. C. Loh, “A hybrid AC/DC microgrid and itscoordination control,”
IEEE Trans. Smart Grid , vol. 2, no. 2, pp. 278–286, 2011.[5] D. E. Olivares, A. Mehrizi-Sani, A. H. Etemadi, C. A. Cañizares,R. Iravani, M. Kazerani, A. H. Hajimiragha, O. Gomis-Bellmunt,M. Saeedifard, R. Palma-Behnke et al. , “Trends in microgrid control,”
IEEE Trans. Smart Grid , vol. 5, no. 4, pp. 1905–1919, 2014.[6] M. Fathi and H. Bevrani, “Statistical cooperative power dispatching ininterconnected microgrids,”
IEEE Trans. Softw. Eng. , vol. 4, no. 3, pp.586–593, 2013.[7] W.-Y. Chiu, H. Sun, and H. V. Poor, “A multiobjective approach tomultimicrogrid system design,”
IEEE Trans. Smart Grid , vol. 6, no. 5,pp. 2263–2272, 2015.[8] W. Zhang, Y. Xu, Z. Dong, and K. P. Wong, “Robust securityconstrained-optimal power flow using multiple microgrids for correctivecontrol of power systems under uncertainty,”
IEEE Trans. Ind. Informat. ,vol. 13, no. 4, pp. 1704–1713, 2017.[9] S. Chanda and A. K. Srivastava, “Defining and enabling resiliency ofelectric distribution systems with multiple microgrids,”
IEEE Trans.Smart Grid , vol. 7, no. 6, pp. 2859–2868, Nov. 2016.[10] B. Zhao, X. Wang, D. Lin, M. M. Calvin, J. C. Morgan, R. Qin, andC. Wang, “Energy management of multiple microgrids based on a systemof systems architecture,”
IEEE Trans. Power Syst. , vol. 33, no. 6, pp.6410–6421, 2018.[11] F. Luo, G. Ranzi, S. Wang, and Z. Y. Dong, “Hierarchical energymanagement system for home microgrids,”
IEEE Trans. Smart Grid ,2018.[12] F. Luo, G. Ranzi, C. Wan, Z. Xu, and Z. Y. Dong, “A multistage homeenergy management system with residential photovoltaic penetration,”
IEEE Trans. Ind. Informat. , vol. 15, no. 1, pp. 116–126, 2019.[13] N. G. Paterakis, O. Erdinç, I. N. Pappi, A. G. Bakirtzis, and J. P. S.Catalão, “Coordinated operation of a neighborhood of smart householdscomprising electric vehicles, energy storage and distributed generation,”
IEEE Trans. Smart Grid , vol. PP, no. 99, pp. 1–12, 2016.[14] N. Nikmehr and S. N. Ravadanegh, “Optimal power dispatch of multi-microgrids at future smart distribution grids,”
IEEE Trans. Smart Grid ,vol. 6, no. 4, pp. 1648–1657, Jul. 2015.[15] C. Zhang, Y. Xu, Z. Y. Dong, and K. P. Wong, “Robust coordination ofdistributed generation and price-based demand response in microgrids,”
IEEE Trans. Smart Grid , vol. 9, no. 5, pp. 4236–4247, 2018.[16] J. Ni and Q. Ai, “Economic power transaction using coalitional gamestrategy in micro-grids,”
IET Gener. Transm. Distrib. , vol. 10, no. 1, pp.10–18, 2016.[17] J. Li, Y. Liu, and L. Wu, “Optimal operation for community based multi-party microgrid in grid-connected and islanded modes,”
IEEE Trans.Smart Grid , vol. 9, no. 2, pp. 756–765, 2018.[18] Z. Wang, B. Chen, J. Wang, M. M. Begovic, and C. Chen, “Coordinatedenergy management of networked microgrids in distribution systems,”
IEEE Trans. Smart Grid , vol. 6, no. 1, pp. 45–53, 2015.[19] S. A. Arefifar, M. Ordonez, and Y. A.-R. I. Mohamed, “Energy manage-ment in multi-microgrid systems-Development and assessment,”
IEEETrans. Power Syst. , vol. 32, no. 2, pp. 910–922, 2017.[20] A. Ouammi, H. Dagdougui, L. Dessaint, and R. Sacile, “Coordinatedmodel predictive-based power flows control in a cooperative network ofsmart microgrids,”
IEEE Trans. Smart Grid , vol. 6, no. 5, pp. 2233–2244, 2015.[21] B. Celik, R. Roche, D. Bouquain, and A. Miraoui, “Decentralizedneighborhood energy management with coordinated smart home energysharing,”
IEEE Trans. Smart Grid , vol. 9, no. 6, pp. 6387–6397, 2018.[22] D. Papadaskalopoulos, D. Pudjianto, and G. Strbac, “Decentralizedcoordination of microgrids with flexible demand and energy storage,”
IEEE Trans. Sustain. Energy , vol. 5, no. 4, pp. 1406–1414, 2014. [23] S. Drouilhet, B. Johnson, S. Drouilhet, and B. Johnson, “A battery lifeprediction method for hybrid power applications,” in , 1997, p. 948.[24] C. Ju, P. Wang, L. Goel, and Y. Xu, “A two-layer energy managementsystem for microgrids with hybrid energy storage considering degrada-tion costs,” IEEE Trans. Smart Grid , vol. 9, no. 6, pp. 6047–6057, Nov.2018.[25] T. Ding, Y. Lin, G. Li, and Z. Bie, “A new model for resilient distributionsystems by microgrids formation,”
IEEE Trans. Power Syst. , 2017.[26] C. Chen, J. Wang, F. Qiu, and D. Zhao, “Resilient distribution system bymicrogrids formation after natural disasters,”
IEEE Trans. Smart Grid ,vol. 7, no. 2, pp. 958–966, 2016.[27] M. A. Kashem, V. Ganapathy, G. B. Jasmon, and M. I. Buhari, “A novelmethod for loss minimization in distribution networks,” in , 2000, pp. 251–256.[28] R. A. Jabr, R. Singh, and B. C. Pal, “Minimum loss network reconfig-uration using mixed-integer convex programming,”
IEEE Trans. PowerSyst. , vol. 27, no. 2, pp. 1106–1115, 2012.[29] K. Turitsyn, P. Sulc, S. Backhaus, and M. Chertkov, “Options for controlof reactive power by distributed photovoltaic generators,”
Proceedingsof the IEEE , vol. 99, no. 6, pp. 1063–1073, 2011.[30] R. A. Jabr, “Linear decision rules for control of reactive power by dis-tributed photovoltaic generators,”
IEEE Transactions on Power Systems
IEEE Trans. Smart Grid ,vol. 5, no. 4, pp. 1864–1875, 2014.[36] W. Hu, P. Wang, and H. B. Gooi, “Toward optimal energy managementof microgrids via robust two-stage optimization,”
IEEE Trans. SmartGrid , vol. 9, no. 2, pp. 1161–1174, 2018.[37] F. Valencia, D. Sáez, J. Collado, F. Ávila, A. Marquez, and J. J. Espinosa,“Robust energy management system based on interval fuzzy models,”
IEEE Trans. Control Syst. Technol. , vol. 24, no. 1, pp. 140–157, 2016.[38] A. R. Malekpour and A. Pahwa, “Stochastic networked microgrid energymanagement with correlated wind generators,”